Which algorithm to use to solve this optimization problem?
A possible approach would be starting by grouping the actions into all possible groups.
For 30 actions grouped in a maximum of 6 this would mean:
$$
C^{30}_6 + C^{30}_5 + C^{30}_4 + C^{30}_3 + C^{30}_2 + C^{30}_1 = 768 211 
$$
Operations.

Then, I would define the constraints to simplify the problem, as in a Constraint Satisfaction Problem (CSP). The main constraint that you have is that one action can only be represented in one Operation. So, if you choose 1 of the 768ks operations to start with, the second option will be restricted by the condition.

Then I would do some sort of planning and sum the costs until the end doing a depth-first search. Whenever I find a total cost better the previous best, you would update the best value. (Remember that the search ends when between all the operations used, all the actions were explored once.)

While doing the search the costs are added up on the go. You can precompute a vector with the same size as the number of operations where each value corresponds to the total cost of the operation, and then sum it as you are going down the path.

You should also add some heuristic to prevent checking the same operations in different orders. For example doing operating [2,3,4] followed by [7,10], where each number represents an action, is the same as doing: [7,10] followed by [2,3,4].